If your date is in A,
First day of the previous month: =DATE(YEAR(A1);MONTH(A1)-1;1)
Last day of the previous month: =A1-DAY(A1)
If your reference day is now,
First day of the previous month: =DATE(YEAR(TODAY());MONTH(TODAY())-1;1)
Last day of the previous month: =TODAY()-DAY(TODAY())